Solve for $t$. $16-2t=\dfrac32t+9$ $t=$
Solution: We need to manipulate the equation to get $ t $ by itself. 16 − 2 t 16 − 2 t − 3 2 t − 7 2 t + 16 − 7 2 t + 16 − 16 − 7 2 t − 7 2 t ⋅ ( − 2 7 ) t t = 3 2 t + 9 = 3 2 t + 9 − 3 2 t = 9 = 9 − 16 = − 7 = − 7 ⋅ ( − 2 7 ) = 14 7 = 2 Subtract 3 2 t from each side. Combine like terms. Subtract 16 from each side. Combine like terms. Multiply each side by - 2 7. Simplify. \begin{aligned} 16-2t&=\dfrac32t+9 \\\\ 16-2t {-\dfrac32t} &= \dfrac32t+9{-\dfrac32t} &&\gray{\text{Subtract }\dfrac32 t \text{ from each side.}}\\\\ -\dfrac72t+16&=9 &&\gray{\text{Combine like terms.}}\\\\ -\dfrac72t+16{-16} &= 9{-16} &&\gray{\text{Subtract 16 from each side.}}\\\\ -\dfrac72t &=-7 &&\gray{\text{Combine like terms.}}\\\\ -\dfrac{7}{2}t\cdot\left({-\dfrac{2}{7}}\right) &= -7\cdot\left({-\dfrac{2}{7}}\right) &&\gray{\text{Multiply each side by -}\dfrac{2}{7}.}\\\\ t&=\dfrac{14}{7}\\\\\ t &= {2} &&\gray{\text{Simplify.}}\\\\ \end{aligned} The answer: $ t= { 2 }~~~~~~~~$ [Let's check our work!]